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Parametrical Study of Free Vibration and Plastic Collapse of a Clamped Beam

DOI: 10.2478/v10147-011-0035-7

Keywords: FEM, Updated Lagrangian Formulation, Von Mises Material Model, Multilinear Isotropic Hardening, Internal Damping

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Abstract:

In this paper a parametrical study of free vibration and plastic collapse of a clamped beam is presented. In the numerical study the finite element method was used utilising the updated Lagrangian formulation for large deformations/large strains, the Von Mises material model with multilinear isotropic hardening for hypoelastic-plastic materials, the Kelvin-Voight's model for internal damping and the Jaumann's objective rate in the form of the Green-Naghdi's objective rate for co-rotational Cauchy's stress update calculation, in which appropriate rotation tensors were expressed with the Rodrigues' formula. The aim of this study was to numerically determine the range of the material parameters of the Kelvin-Voight's damping model using a real material, such as low carbon steel, which is a commonly used construction material in contemporary engineering practice. In the numerical experiments elastic and plastic loading cases were studied applying pressure on the upper surface of the bar free end as stepped load using the Heaviside step function. A few relevant results of the study are presented and briefly discussed too.

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